X^2-2x^2+x=0

Solution for X^2-2x^2+x=0 equation:

Simplifying
X2 + -2x2 + x = 0

Reorder the terms:
X2 + x + -2x2 = 0

Solving
X2 + x + -2x2 = 0

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-1x' to each side of the equation.
X2 + x + -1x + -2x2 = 0 + -1x

Combine like terms: x + -1x = 0
X2 + 0 + -2x2 = 0 + -1x
X2 + -2x2 = 0 + -1x
Remove the zero:
X2 + -2x2 = -1x

Add '2x2' to each side of the equation.
X2 + -2x2 + 2x2 = -1x + 2x2

Combine like terms: -2x2 + 2x2 = 0
X2 + 0 = -1x + 2x2
X2 = -1x + 2x2

Simplifying
X2 = -1x + 2x2

Reorder the terms:
X2 + x + -2x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
X2 + x + -2x2 = 0 + 2x2 + -2x2
X2 + x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
X2 + x + -2x2 = 0

Factor a trinomial.
(X + -1x)(X + 2x) = 0

Subproblem 1
Set the factor '(X + -1x)' equal to zero and attempt to solve:

Simplifying
X + -1x = 0

Solving
X + -1x = 0

Move all terms containing X to the left, all other terms to the right.

Add 'x' to each side of the equation.
X + -1x + x = 0 + x

Combine like terms: -1x + x = 0
X + 0 = 0 + x
X = 0 + x
Remove the zero:
X = x

Simplifying
X = x
Subproblem 2
Set the factor '(X + 2x)' equal to zero and attempt to solve:

Simplifying
X + 2x = 0

Solving
X + 2x = 0

Move all terms containing X to the left, all other terms to the right.

Add '-2x' to each side of the equation.
X + 2x + -2x = 0 + -2x

Combine like terms: 2x + -2x = 0
X + 0 = 0 + -2x
X = 0 + -2x
Remove the zero:
X = -2x

Simplifying
X = -2x
Solution
X = {x, -2x}